Posted on 02/16/2007 11:23:52 PM PST by neverdem
I live in Alaska, please in the future keep my winter above zero and my summer below 85, thank you.
Three hours plus and counting. Not stuck are you?
stuck?... lol... you really are into games, aren't you?
You are absolutely right, but to answer your next question too. Newton's equation GmM/r2 is accurate to one part in 107. Newtons basic equations may not be 100% accurate but Einstein didn't 'disprove' them either.
I think anyone who doesn't know the difference between two of the greatest scientific ideas of the past century should keep his mouth shut about science.
Kind of hard to argue against that logic :) I just prefer to give him the benefit of the doubt on the date.
I found the hypothesis that a warming environment might ameliorate the weather to be interesting. For some reason I had just bought into the propaganda that a warming climate would create much worse weather. I just assumed that more energy in the system would create more chaos. I need to be more skeptical than I am.
Pleaaaaase tell me the answer to the puzzle? I didn't quite get it... They EITHER gets 1 or 0??
No, they get a random number from zero to one (inclusive) but no number in that range is preferred to any other, that's what "uniform" means. For example, you might get 0.5 or 0.34598231 or 0.99991413872 etc. But of course the likelihood is zero of getting a number with finite precision like that because such numbers are so few compared to all the real numbers in the range.
One way to think of it is as a limit of a sequence of finite sets of numbers. For example, a finite instance would be to get a random decimal fraction between zero and one with 100 or 200 or 1000000 digits of precision and then let the amount of precision grow very large.
If you wanted to simulate the game very closely in a program, you'd use a random number generator, let's say one that produces integers from zero to 232-1 and then divide by 232 to obtain a fraction. Both players get one and they can keep it or turn it in a draw another random number the same way. The numbers they end up with are compared and whoever has the greater one wins.
And so the puzzle is to devise a strategy a player can follow to ensure he wins with probablility at least 1/2 no matter what strategy the other player follows.
I don't see how that can be true, that the discrepancy can be no larger. The masses can presumably be increased without limit and I bet that for a given r there's some large mass that the error would be larger.
But there are errors in kind too where Newton would predict zero effect but Einstein predicts non-zero and in such a case the error is infinite. For example, if a mass is rotating, it actually makes spacetime rotate too. A test mass falling toward the "equator" of the rotating one would appear to a distant observer to move laterally. Newton would have the test mass fall straight toward the other.
Everybody on this thread sees that you've called me a dim bulb but aren't able to solve a problem I did in a few hours. Pathetic but amusingly so.
Yup, you just blew my synapses. This is exactly the reason why I choose to go to law school...no math.
Could be. Increased clouds without an increase in water-vapor level (hard to get, but comic rays or dust could do it) will lower the temperature, I think. Increased water-vapor without clouds, possible at lower dew-points, should increase temperature.
No. He's making known it's source. I get the impression from you that unless someone has a degree in physics, then any commentary on global warming isn't worth the time of day.
I didn't bother to read further.
I find it interesting that the person who made that comment is still making more comments on this thread.
Anyone who thinks if the predictions work out, we can regard the hypothesis as proven just doesn't get it.
How did the laws of motion and thermodynamics start, as manna from On High?
So, he got the year wrong -- why on earth would that mean he doesn't have a clue? He said at the beginning he was quoting Rush -- why screw up the quote by sweating a small thing like the wrong year?
It's worth noting that a new theory (e.g., Special Relativity replacing Newton's equations of motion) must account for all the existing valid data that the previous theory predicted, as well as new effects, and make predictions that later are seen to be true. That is quite a tall order.
That reminds me, did you hear that Mars once had water on it and now is like a desert? Some kind of marcian warming must have taken place. As of yet scientists have not been able to discover the SUVs that may have been responsible for the warming. Stay tuned.
This is not a reasonable way for a physicist to look at it. Newtons's result for the classical equation of motion is regarded as a limiting value of the Einstein result from special relativity. In other words, it is the value of the special-relativity equation of motion in the limit of v/c going to zero. There is no 'infinite error'.
I would agree with this assessment. Perhaps except for the zero. Probability seldom reaches the asymptote.
But just as Keynesian Economics ruled politics for many decades, the anti-science attitudes of today may slowly erode as science does its slow and steady work to solve problems which will not yield to political pressure.
Glacially, perhaps, the realization that we need a larger presence in space may penetrate even the brie and croissant crowd in Washington.
In reluctant recognition that the sun may have something to do with their indisputable Global Warming, they may allow activities intended to ameliorate the effect. It is, after all, hard to blame global warming on Mars on those ubiquitous SUVs here.
You might find this interesting.
As seen from Earth the precession of Mercury's orbit is measured to be 5600 seconds of arc per century (one second of arc=1/3600 degrees). Newton's equations, taking into account all the effects from the other planets (as well as a very slight deformation of the sun due to its rotation) and the fact that the Earth is not an inertial frame of reference, predicts a precession of 5557 seconds of arc per century. There is a discrepancy of 43 seconds of arc per century.An error of 43 out of 5557 is nearly one part in 10^2. So I guess I'm not sure what you meant.
Actually, it may have been the gradual cooling that was to blame for Mars losing its water. Ice ages promote desertification.
As the atmosphere thinned and cooled, what water vapor was in it may have dissociated under sunlight in the upper atmosphere, and been carried away on the solar wind.
Very likely Jupiter, greedy scavenger that it is, gobbled up the majority of that water, but it is possible that some of it could have fallen to Earth. Those heavily invested in Noah's flood may like this idea.
I've been pushing the notion that if global flooding due to melting icecaps is the fear, we should send our excess water to Mars to replenish its oceans. More could be obtained from the icy rings of Saturn as well. It would be the first step toward terraforming Mars.
I didn't mean to give that impression. I don't have one but I have some interesting things to say nonetheless. The difference being that I know what I don't know and don't pretend otherwise.
I find it interesting that the person who made that comment is still making more comments on this thread.
The responses can be interesting or amusing. For example the guy who called me a dim bulb but is unable to solve a problem I could in a few hours. But also one of the other posters made some good points. I guess you could say the thread is lot's more informative than the article.
How did the laws of motion and thermodynamics start, as manna from On High?
Scientific laws are derived from observation, they are straight forward extrapolations of those observations. They are not explanatory in the way that hypotheses and theories are. So I'm not sure why you bring these two up when clearly we are talking about hypotheses and theories.
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